1. Field of the Invention
The present invention relates to optical instruments and methods for aiming a rifle, external ballistics and methods for predicting a gyroscopically stabilized projectile's trajectory to a target. This application relates to projectile weapon aiming systems such as rifle scopes, to reticle configurations for projectile weapon aiming systems, and to associated methods of compensating for a projectile's external ballistic behavior while developing a field expedient firing solution.
2. Discussion of the Prior Art
Rifle marksmanship has been continuously developing over the last few hundred years, and now refinements in materials and manufacturing processes have made increasingly accurate aimed fire possible. These refinements have made previously ignored environmental and external ballistics factors more significant as sources of aiming error.
The term “rifle” as used here, means a projectile controlling instrument or weapon configured to aim and propel or shoot a projectile, and rifle sights or projectile weapon aiming systems are discussed principally with reference to their use on rifles and embodied in telescopic sights commonly known as rifle scopes. It will become apparent, however, that projectile weapon aiming systems may include aiming devices other than rifle scopes, and may be used on instruments or weapons other than rifles which are capable of controlling and propelling projectiles along substantially pre-determinable trajectories (e.g., rail guns or cannon). The prior art provides a richly detailed library documenting the process of improving the accuracy of aimed fire from rifles (e.g., as shown in FIG. 1A) and other firearms or projectile weapons.
Most shooters or marksmen, whether hunting or target shooting, understand the basic process for aiming. The primary aiming factors are (a) elevation, for range or distance to the target or Point of Aim (“POA”), where the selected elevation determines the arcuate trajectory and “drop” of the bullet in flight and the Time of Flight (“TOF”), and (b) windage, because transverse or lateral forces act on the bullet during TOF and cause wind deflection or lateral drift. All experienced marksmen account for these two factors when aiming. Precision long-range shooters such as military and police marksmen (or “snipers”) often resort to references including military and governmental technical publications such as the following:    (Ref 1) Jonathan M. Weaver, Jr., LTC, USA Ret., Infantry, System Error Budgets, Target Distributions and Hitting Performance Estimates for General-Purpose Rifles and Sniper Rifles of 7.62×51 mm and Larger Calibers, AD-A228 398, TR-461, AMSAA, May, 1990;    (Ref 2) McCoy, Robert L., A Parametric Study of the Long Range, Special Application Sniper Rifle, Aberdeen Proving Grounds (“APG”), MD, BRL Memorandum Report No. 3558, December 1986;    (Ref 3) Brophy, William S., Maj., Ord., A Test of Sniper Rifles, 37th Report of Project No. TS2-2015, APG, MD D&PS, 27 Jul. 1955;    (Ref 4) Von Wahlde, Raymond & Metz, Dennis, Sniper Weapon Fire Control Error Budget Analysis, US Army ARL-TR-2065, August, 1999-arl.army.mil;    (Ref 5) US Army FM-23-10, Sniper Training, United States Army Infantry School ATSH-IN-S3, Fort Benning, Ga. 31905-5596, August 1994; and    (Ref 6) USMC MCWP 3-15.3 (formerly FMFM 1-3B), Sniping, PCN 143 000118 00, Doctrine Division (C42) US Marine Corps Combat Development Command, 2 Broadway Street Suite 210 Quantico, Va. 22134-5021, May 2004.For nomenclature purposes and to provide a more complete background and foundation for what follows, these published references are incorporated herein by reference.
A number of patented rifle sights or projectile weapon aiming systems have been developed to help marksmen account for the elevation/range and windage factors when aiming. For example, U.S. Pat. No. 7,603,804 (to Zadery et al) describes a riflescope made and sold by Leupold & Stevens, Inc., with a reticle including a central crosshair defined as the primary aiming mark for a first selected range (or “zero range”) and further includes a plurality of secondary aiming marks spaced below the primary aiming mark on a primary vertical axis. Zadery's secondary aiming marks are positioned to compensate for predicted ballistic drop at selected incremental ranges beyond the first selected range, for identified groups of bullets having similar ballistic characteristics.
Zadery's rifle scope has variable magnification, and since Zadery's reticle is not in the first focal plane (“F1”) the angles subtended by the secondary aiming marks of the reticle can be increased or decreased by changing the optical power of the riflescope to compensate for ballistic characteristics of different ammunition. The rifle scope's crosshair is defined by the primary vertical line or axis which is intersected by a perpendicular horizontal line or primary horizontal axis. The reticle includes horizontally projecting windage aiming marks on secondary horizontal axes intersecting selected secondary aiming marks, to facilitate compensation for the effect of crosswinds on the trajectory of the projectile at the selected incremental ranges At each secondary aiming mark on the primary vertical axis, the laterally or horizontally projecting windage aiming marks project symmetrically (left and right) from the vertical axis, indicating a windage correction for wind from the shooter's right and left sides, respectively.
Beyond bullet drop over a given range and basic left-right or lateral force windage compensation, there are several other ballistic factors which result in lesser errors in aiming. As the inherent precision of rifles and ammunition improves, it is increasingly critical that these other factors be taken into consideration and compensated for, in order to make an extremely accurate shot. These factors are especially critical at very long ranges, (e.g., approaching or beyond one thousand yards). Many of these other factors were addressed in this applicant's U.S. Pat. No. 7,325,353 (to Cole & Tubb) which describes a riflescope reticle including a plurality of charts, graphs or nomographs arrayed so a shooter can solve the ranging and ballistic problems required for correct estimation and aiming at a selected target. The '353 patent's scope reticle includes at least one aiming point field to allow a shooter to compensate for range (with elevation) and windage, with the “vertical” axis precisely diverging to compensate for “spin drift” and precession at longer ranges. Stadia for determining angular target dimension(s) are included on the reticle, with a nomograph for determining apparent distance from the apparent dimensions being provided either on the reticle or external to the scope. Additional nomographs are provided for the determination and compensation of non-level slopes, non-standard density altitudes, and wind correction, either on the reticle or external to the riflescope.
The elevation and windage aim point field (50) in the '353 patent's reticle is comparable, in one respect, to traditional bullet drop compensation reticles such as the reticle illustrated in the Zaderey '804 patent, but includes a number of refinements such as the compensated elevation or “vertical” crosshair 54, which can be seen to diverge laterally away from a true vertical reference line 56 (e.g., as shown in FIG. 3 of the '353 patent), to the right (i.e., for a rifle barrel with rifling oriented for right hand twist). The commercial embodiment of the '353 patent reticle is known as the DTAC™ Reticle, and the RET-2 version of the DTAC reticle is illustrated in FIG. 1C.
The compensated elevation or “vertical” crosshair of the DTAC™ reticle is useful for estimating the ballistic effect of the bullet's gyroscopic precession or “spin drift” caused by the bullet's stabilizing axial rotation or spin, which is imparted on the bullet by the rifle barrel's inwardly projecting helical “lands” which bear upon the bullet's circumferential surfaces as the bullets accelerates distally down the barrel. Precession or “spin drift” is due to an angular change of the axis of the bullet in flight as it travels an arcuate ballistic flight path. While various corrections have been developed for most of these factors, the corrections were typically provided in the form of programmable electronic devices or earlier in the form of logbooks developed over time by precision shooters. Additional factors affecting exterior ballistics of a bullet in flight include atmospheric variables, specifically altitude and barometric pressure, temperature, and humidity.
Traditional telescopic firearm sight reticles have been developed with markings to assist the shooter in determining the apparent range of a target. A nearly universal system has been developed by the military for artillery purposes, known as the “milli-radian,” or “mil,” for short. This system has been adopted by most of the military for tactical (e.g., sniper) use, and was subsequently adopted by most of the sport shooting world. The mil is an angle having a tangent of 0.001. A mil-dot scale is typically an array of dots (or similar indicia) arrayed along a line which is used to estimate or measure the distance to a target by observing the apparent target height or span (or the height or span of a known object in the vicinity of the target). For example, a target distance of one thousand yards would result in one mil subtending a height of approximately one yard, or thirty six inches, at the target. This is about 0.058 degree, or about 3.5 minutes of angle. It should be noted that although the term “mil-radian” implies a relationship to the radian, the mil is not exactly equal to an angle of a single one thousandth of a radian, which would be about 0.057 degree or about 3.42 minutes of angle. The “mil-dot” system, based upon the mil, is in wide use in scope reticle marking, but does not provide a direct measure for determining the distance to a target without first having at least a general idea of the target size, and then performing a mathematical calculation involving these factors. Confusingly, the US Army and the US Marine Corps do not agree on these conversions exactly (see, e.g., Refs 5 and 6), which means that depending on how the shooter is equipped, the shooter's calculations using these conversions may change slightly.
The angular measurement known as the “minute of angle,” or MOA is used to measure the height or distance subtended by an angle of one minute, or one sixtieth of one degree. At a range of one hundred yards, this subtended angle spans slightly less than 1.05 inches, or about 10.47 inches at one thousand yards range. It will be seen that the distance subtended by the MOA is substantially less than that subtended by the mil at any given distance, i.e. thirty six inches for one mil at one thousand yards but only 10.47 inches for one MOA at that range. Thus, shooters have developed a rather elaborate set of procedures to calculate required changes to sights (often referred to as “clicks”) based on a required adjustment in a bullet's point of impact (e.g., as measured in “inches” or “minutes”).
Sight adjustment and ranging methods have been featured in a number of patents Assigned to Horus Vision, LLC, including U.S. Pat. Nos. 6,453,595 and 6,681,512, each entitled “Gunsight and Reticle therefore” by D. J. Sammut and, more recently, U.S. Pat. No. 7,832,137, entitled “Apparatus and Method for Calculating Aiming Point Information” by Sammut et al. These patents describe several embodiments of the Horus Vision™ reticles, which are used in conjunction with a series of calculations to provide predicted vertical corrections (or holdovers) for estimated ranges and lateral corrections (or windage adjustments), where a shooter calculates holdover and windage adjustments separately, and then selects a corresponding aiming point on the reticle.
In addition to the general knowledge of the field of the present invention described above, the applicant is also aware of certain foreign references which relate generally to the invention. Japanese Patent Publication No. 55-36,823 published on Mar. 14, 1980 to Raito Koki Seisakusho KK describes (according to the drawings and English abstract) a variable power rifle scope having a variable distance between two horizontally disposed reticle lines, depending upon the optical power selected. The distance may be adjusted to subtend a known span or dimension at the target, with the distance being displayed numerically on a circumferential external adjustment ring. A prism transmits the distance setting displayed on the external ring to the eyepiece of the scope, for viewing by the marksman.